Category: Chemical Engineering Math
"Published in Newark, California, USA"
Calculate the molar concentration of a solution that is 30% wt. NH4NO3 and has a specific gravity of 1.1252.
Solution:
The concentration of a given solution by percent of weight can be written as follows
Since the specific gravity of a solution which is also the density of a solution is given in the problem, then we can express the concentration of a solution in grams of NH4NO3 per liter of solution as follows
The molarity of a solution is defined as moles of solute per liter of solution. Therefore, the molarity of NH4NO3 solution is
Category: Chemical Engineering Math
"Published in Newark, California, USA"
What is the normality of a sulfuric acid solution that is 18 M?
Solution:
The molarity of a solution is defined as moles of solute per liter of solution. The given concentration of sulfuric acid solution can be written as follows
Let's consider the ionization of sulfuric acid as follows
Hydrogen ion has an oxidation number of 1 and sulfate ion has an oxidation number of 2. The number of equivalence of a solute is defined as the product of the number of positive ions in a metal ion and the number of negative ions in a non-metal ion. In this case, the number of equivalence of sulfuric acid is 1 x 2 = 2.
The normality of a solution is defined as the number of equivalence of a solute per liter of solution.
Therefore, the normality of a sulfuric acid solution is
Category: Chemical Engineering Math, Differential Equations
"Published in Newark, California, USA"
How old is a bottle of wine if the tritium 3H content is 45% of a new wine? The half-life of tritium is 12.5 years.
Solution:
From the
description of a given problem, it is about exponential decay problem.
The rate of change of a substance is directly proportional to the
negative of its substance present. The working equation can be expressed
as follows
where
x = amount of tritium at time t
t = decaying time of tritium
k = proportional constant for decaying
By separation of variables, transfer x to the left side of the equation and dt to the right side of the equation as follows
Integrate on both sides of the equation, we have
Take the inverse natural logarithm on both sides of the equation, we have
If x = x0 and t = 0 at the start, then the value of C is
Hence, the particular solution of the working equation is
If x = ½ x0 at t = 12.5 years, then the value of k is
Take natural logarithm on both sides of the equation, we have
Hence, the complete working equation of the above equation is
If x = 0.45 x0 as stated in the problem, therefore, the age of a bottle of wine that contains tritium is
Take the natural logarithm on both sides of the equation,w e have
